Multivariable Calculus – Jon Rogawski – 2nd Edition

Chapter 12: Vector Geometry
12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
12.5 Planes in Three-Space
12.6 A Survey of Quadric Surfaces
12.7 Cylindrical and Spherical Coordinates

Chapter 13: Calculus of Vector-Valued Functions
13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in Three-Space
13.6 Planetary Motion According to Kepler and Newton

Chapter 14: Differentiation in Several Variables
14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.3 Partial Derivatives
14.4 Differentiability and Tangent Planes
14.5 The Gradient and Directional Derivatives
14.6 The Chain Rule
14.7 Optimization in Several Variables
14.8 Lagrange Multipliers: Optimizing with a Constraint

Chapter 15: Multiple Integration
15.1 Integration in Variables
15.2 Double Integrals over More General Regions
15.3 Triple Integrals
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
15.5 Applications of Multiplying Integrals
15.6 Change of Variables

Chapter 16: Line and Surface Integrals
16.1 Vector Fields
16.2 Line Integrals
16.3 Conservative Vector Fields
16.4 Parametrized Surfaces and Surface Integrals
16.5 Surface Integrals of Vector Fields

Chapter 17: Fundamental Theorems of Vector Analysis
17.1 Green’s Theorem
17.2 Stokes’ Theorem
17.3 Divergence Theorem